Determining the Route of Trace Elements Through Inter-connected Systems

Project Overview and Motivation

The existence of certain chemicals within a system
can provide useful indications of other potentially dangerous pollutants. For example, the proportion of Carbon-14 in the atmosphere could potentially be used to indicate the proportion of CO2 increase due to fossil fuels and cement production. Despite such beneficial implications, the calculations used for determining Carbon-14 levels are not so clear. Modelling the atmosphere as a single, well mixed reservoir, we can interpret Carbon-14 as a trace element – a chemical element existing only in minute amounts in a given environment. The atmosphere participates in relatively small exchanges with other reservoirs such as ground biomass, forestry, the ocean and Phytoplankton. The issue of efficiently modelling the routes and concentration of Carbon-14 can be generalised to many other problems regarding pollutants and mixing. In this article we focus attention upon situations in which a small trace is added to one reservoir of many, each with relatively small interactions with other reservoirs.

The method of generalization we will employ in this article consists of modelling the route and concentration of a single drop of dye as it progresses through a complex system of pools. Here, the reservoirs in question are modelled by a system of inter-connected swimming pools, each with individual starting volumes and capacities. We model the exchange of fluid by instantaneous pumps with individual flow-rates between pairs of pools. Our independent variables therefore consists of, but are not limited to, the number of pools within the system, the maximum capacity of each pool, the flow rates of the pumps and their corresponding directions.